The Lunar Month

1. The obvious measure of the month is relative to the fixed stars. Start the timing when the Moon passes a star and stop it when the Moon passes it again four weeks later. The problem is that the exact time depends on which star you choose because every star is moving. If it happens to be moving west, the month will be a little shorter than average; if moving east it will be a little longer than average. This is called the Sidereal Month, and averages 27.32166 days (27 days, 7 hours, 43 minutes, 11.6 seconds).
2. The second way that may seem obvious is to measure the time between one New Moon (or Full Moon, or any other defined phase) and the next. This is slightly different month to month, but averages 29.53059 days (29 days, 12 hours, 44 minutes, 2.8 seconds) and is called the Synodic Month. The reason for the extra two days is that while the Moon was revolving round the Earth, the Sun had moved on approximately 30 degrees in its annual orbit around the Earth, (I realise we normally think of the Earth revolving around the Sun, but here we are looking at the system from the point of view of the Earth so it is simpler to think of the Sun revolving around the Earth once a year.) It takes the Moon that extra 2 and a bit days to catch up with the Sun.
3. The third way we might measure the month is to note that the Moon's orbit is elliptical with the Earth at one focus. So we could take the time from when the Moon passes the point in its orbit closest to the Earth, the perigee, until it returns there. This is known as the Anomalistic Month and on average is 27.55455 days long (27 days, 13 hours, 18 minutes, 33.1 seconds). This is slightly longer than the sidereal month because the major axis of the Moon's orbit is precessing in a prograde direction (the same direction that the Moon is revolving).
4. The Moon's orbit in not in the plane of the ecliptic (the plane of the Earth's orbit around the Sun) so there are two points, called nodes, where the Moon's orbit crosses the plane of the ecliptic. We can measure the month relative to one of these points. This is called the Draconic Month and averages 27.21222 days (27 days, 5 hours, 5 minutes, 35.8 seconds). This is slightly shorter than the sidereal month because the plane of the orbit is precessing in a retrograde direction (the opposite direction to the Moon).
5. Finally we note that the Moon's rotational axis is not at right angles to its orbit, so, as it revolves around the Earth, the Sun moves north and south of the lunar equator. This is exactly the same phenomenon as causes summer and winter on the Earth. We can measure the month from one of the equinoxes when the Sun is directly over the lunar equator. This is the Tropical Month and is 27.32158 days long (27 days, 7 hours, 43 minutes, 4.5 seconds). Of course the Moon's rotational axis is also precessing. Nothing is fixed in the sky.

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